The sine function is a smooth, continuous function, so we can go ahead and move right to direct substitution.
Using our trigonometry skills leads to our solution.
sin(2π) = 0
When approaching 2 from the right, the limit is 0.
Example 2
Evaluate .
It doesn't matter how tall of a fraction we have, we'll still try to stick our limit in there.
Success.
Example 3
Evaluate .
We're only asked to evaluate this limit as we approach 3 from the right, so we only need to focus on the values when x is greater than 3. Limits don't care about what actually happens at the value it's approaching. The rest of the function doesn't even register for them.
Direct substitution now works well for our continuous function.
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